For all positive integers n, the symbol n! denotes the product of the first n positive integers. In other words, 4! = 4x3x2x1 = 24.
Find the value of n for which
(3!)(5!)(7!) = n!
Solution: The answer is 10.
Notice that (3!)(5!) = (6)(120) = 720 = 8*9*10.
then, (7!)(3!)(5!) = (7!)(8*9*10) = 10!
and n = 10.
Correctly solved by:
| 1. Keith Mealy | Cincinnati, Ohio |
| 2. Rick Jones | Kennett Square, Pennsylvania |
| 3. Sean Giddings | Shawnee Mission, Kansas |
| 4. Carter Wallace | Columbus, Georgia |
| 5. Richard K. Johnson | La Jolla, California |
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| 7. Walt Arrison | Philadelphia, Pennsylvania |
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| 9. John Beasley | Winchester, Virginia |
| 10. Travis Riggs | Winchester, Virginia |
| 11. David Powell | Winchester, Virginia |
| 12. Nick von Keller | Winchester, Virginia |
| 13. John Funk | Ventura, California |
| 14. Bob Hearn | Winchester, Virginia |
| 15. Izzy Kushner | Closter, New Jersey |
| 16. Janine Oliver | Winchester, Virginia |
| 17. Matt Crandell | Winchester, Virginia |
| 18. George Gaither | Winchester, Virginia |
| 19. Laurence O'Neill | Winchester, Virginia |
| 20. Jaime Garcia | Winchester, Virginia |
| 21. Renata Sommerville | Austin, Texas |
| 22. Geoff Keith | Santa Monica, California |
| 23. Justin Collins | Winchester, Virginia |
| 24. Carter Staples | Columbus, Georgia |
| 25. Matt McMurtry | Arlington, Virginia |
| 26. Stevenson Gravlee | Columbus, Georgia |
| 27. Jeffrey Ward | Columbus, Georgia |
| 28. John Lybarger | Calhoun Community College, Alabama |
| 29. Wilds Ogie | Columbus, Georgia |
| 30. Ghazaleh Joukar | Winchester, Virginia |
| 31. Ellen Sankovich | Winchester, Virginia |
| 32. Ashley Maignan | Columbus, Georgia |
| 33. James Alarie | University of Michigan -- Flint |
| 34. Katrina | Lenexa, Kansas |
| 35. Josh Reifsnyder | Winchester, Virginia |
| 36. Jeffrey Bentz | Shawnee Mission, Kansas |